Core Protocol
The Axiom Consensus Protocol is built on a rigorous foundation: universal axioms that AI cannot deny, convergence guaranteed by the golden ratio, and a musical architecture that transforms disagreement into harmony.
This section covers the complete ACP v4.0 specification -- from the philosophical underpinnings through the mathematical guarantees to the concrete algorithm and metrics used in production.
Philosophical Foundation
The central problem of multi-model disagreement, the key insights of universal axioms and self-reference, the Meta-Axiom that AI cannot lie, and truth as a strange attractor.
7 Axiom Levels
The complete axiom hierarchy from Mathematical (Level 1) through Linguistic (Level 7), including self-referential levels that AI cannot deny because it is built upon them.
φ-Convergence
The Axiom Spiral -- how each iteration reduces disagreement by the golden ratio. After 7 loops, only 3.4% divergence remains. Consensus is mathematically guaranteed.
Fugue Architecture
Three musical structures for consensus: Fugue (deep analysis), Sonata (conflict resolution), Concert (creative tasks). Musical intervals as agreement metrics.
Algorithm v4.0
The complete ACP v4.0 consensus algorithm -- from initialization and exposition through spiral loops, stretto compression, and coda. Includes formal consensus criteria.
Metrics
D-score (divergence), C_ij (pairwise agreement), H_total (harmony), oracle verification, musical interval mappings, and criticality-weighted scoring.